JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The equations of two sides of a variable triangle are \(x =0\) and \(y =3\), and its third side is a tangent to the parabola \(y^2=6 x\). The locus of its circumcentre is :
- A \(4 y^2-18 y-3 x-18=0\)
- B \(4 y^2+18 y+3 x+18=0\)
- C \(4 y^2-18 y+3 x+18=0\)
- D \(4 y^2-18 y-3 x+18=0\)
Answer & Solution
Correct Answer
(C) \(4 y^2-18 y+3 x+18=0\)
Step-by-step Solution
Detailed explanation
\(y^2=6 x \quad y^2=4 a x \) \(\Rightarrow 4 a=6 \Rightarrow a=\frac{3}{2}\) \(y = mx +\frac{3}{2 m } ;( m \neq 0)\) \(h =\frac{6 m -3}{4 m ^2}, k =\frac{6 m +3}{4 m }\), Now eliminating \(m\) and we get \(\Rightarrow 3 h=2\left(-2 k^2+9 k-9\right)\)…
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